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Tests of seasonal integration and cointegration in multivariate unobserved component models

  • Fabio Busetti

    (Banca d'Italia)

The paper considers tests of seasonal integration and cointegration for multivariate time series. The locally best invariant (LBI) test of the null hypothesis of a deterministic seasonal pattern against the alternative of seasonal integration is derived for a model with Gaussian i.i.d. disturbances and deterministic trend. A test of seasonal cointegration is then proposed, which parallels the common trend test of Nyblom and Harvey (2000). The tests are subsequently generalized to account for stochastic trends, weakly dependent errors and unattended unit roots. Asymptotic representations and critical values of the tests are provided, while the finite sample performance is evaluated by Monte Carlo simulation experiments. We apply the tests to the indices of industrial production of the four largest countries of the European Monetary Union. We find evidence that Germany does not cointegrate with the other countries, while there seems to exist a common nonstationary seasonal component between France, Italy and Spain.

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Paper provided by EconWPA in its series Econometrics with number 0411003.

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Length: 35 pages
Date of creation: 05 Nov 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0411003
Note: Type of Document - pdf; pages: 35
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  1. Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part I," Econometric Theory, Cambridge University Press, vol. 15(04), pages 435-468, August.
  2. Nyblom, Jukka & Harvey, Andrew, 1999. "Tests of Common Stochastic Trends," Cambridge Working Papers in Economics 9902, Faculty of Economics, University of Cambridge.
  3. Cubadda, Gianluca & Omtzigt, Pieter, 2005. "Small-sample improvements in the statistical analysis of seasonally cointegrated systems," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 333-348, April.
  4. Philip Hans Franses & Michael McAleer, 1998. "Cointegration Analysis of Seasonal Time Series," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 651-678, December.
  5. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  6. Fabio Busetti, 2003. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Temi di discussione (Economic working papers) 476, Bank of Italy, Economic Research and International Relations Area.
  7. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  8. J. Joseph Beaulieu & Jeffrey A. Miron, 1992. "Seasonal Unit Roots in Aggregate U.S. Data," NBER Technical Working Papers 0126, National Bureau of Economic Research, Inc.
  9. Caner, Mehmet, 1998. "A Locally Optimal Seaosnal Unit-Root Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 349-56, July.
  10. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-91, May-June.
  11. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  12. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  13. Huang, Tai-Hsin & Shen, Chung-Hua, 2002. "Seasonal cointegration and cross-equation restrictions on a forward-looking buffer stock model of money demand," Journal of Econometrics, Elsevier, vol. 111(1), pages 11-46, November.
  14. Reimers, Hans-Eggert, 1997. "Seasonal Cointegration Analysis of German Consumption Function," Empirical Economics, Springer, vol. 22(2), pages 205-31.
  15. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
  16. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  17. Ahn, Sung K. & Reinsel, Gregory C., 1994. "Estimation of partially nonstationary vector autoregressive models with seasonal behavior," Journal of Econometrics, Elsevier, vol. 62(2), pages 317-350, June.
  18. Engle, R. F. & Granger, C. W. J. & Hylleberg, S. & Lee, H. S., 1993. "The Japanese consumption function," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 275-298.
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